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## Main Question or Discussion Point

Algebra 5

DecisionProblemsinGroupTheory(L24)................. .............5

LieAlgebrasandRepresentationTheory(M24)............ ...............5

ModularRepresentationsofFiniteGroups(L24).......... ................6

Calculusandalgebra(L24)............................ ..........8

Representationsof?nitegroupsofLietype(L24)......... .................8

CommutativeAlgebra(M24)............................ .........9

Non-commutativealgebras(L24)....................... ............9

VonNeumannAlgebras(L24)............................ .........10

Analysis 12

TopologicalGroups(L24)............................. ..........12

TopicsinIn?niteGroups(M16)......................... ...........12

AnalysisontheDiscreteHypercube(L24)— Non–Examinable .................13

IntroductiontoFunctionalAnalysis(M24).............. ................14

ComplexDi?erentialEquations(L24)................... .............15

Ellipticpartialdi?erentialequations(M24)........... ..................15

Combinatorics 17

Combinatorics(M16)................................. .........17

CombinatorialProbability(L16)...................... .............17

HypergraphGames(E8)— Non–Examinable ..........................18

ArithmeticCombinatorics(M16)....................... ............18

GeometryandTopology 19

TheX-raytransformingeometryanddynamics(L24)........ ...............19

AlgebraicTopology(M24)............................. ..........20

Di?erentialGeometry(M24)........................... ..........20

SpectralGeometry(L24).............................. .........21

AlgebraicGeometry(M24)............................. .........22

ComplexManifolds(L24).............................. .........22

AlgebraicGroups(M24)............................... .........24

FibreBundles(L16).................................. ........24

AlgebraicCycles(L24)............................... ..........25

Logic 26

CategoryTheory(M24)................................ ........26

SetTheoryandLogic(L24)............................. .........27

NumberTheory 29

EllipticCurves(L24)................................ ..........29

LocalFields(M16)................................... ........29

ErgodicTheory(L24)................................. ........30

TheIwasawatheoryofellipticcurveswithcomplexmultiplication(L24).............31

AlgebraicNumberTheory(M16)......................... ..........31

ModularFormsandAutomorphicForms(L24)............... ............32

Non-abelianLubin-Tatetheory(M24)— Non–Examinable ...................32

Probability 3

AdvancedProbability(M24)........................... ..........3

StochasticNetworks(L24)............................ ...........3

StochasticLoewnerEvolutions(L16)................... ..............3

StochasticCalculusandApplications(L24)............. ................3

ParticlePhysics,QuantumFieldsandStrings 46

QuantumFieldTheory(M24)............................ .........46

SymmetryandParticlePhysics(M24).................... ............47

StatisticalFieldTheoryandApplications(M24)......... .................48

AdvancedQuantumFieldTheory(L24).................... ...........49

StringTheory(L24).................................. ........49

SupersymmetryandExtraDimensions(L24)............... .............50

StandardModel(L24)................................. ........51

SolitonsandInstantons(E16)......................... ............52

Supergravity(E16).................................. .........53

3

QuantumInformationandQuantumFoundations 54

IntroductiontoQuantumComputation(M16).............. .............54

QuantumInformation,EntanglementandNonlocality(M16). ..................55

PhilosophyofClassicalandQuantumMechanics(M12,L12).. .................55

MathematicalAspectsofQuantumInformationTheory(L24). ..................56

QuantumControl(L16)................................ ........57

RelativityandGravitation 59

Cosmology(M24)..................................... .......59

GeneralRelativity(M24)............................. ..........61

AdvancedCosmology(L16)............................. .........62

ApplicationsofDi?erentialGeometrytoPhysics(L24).... ...................63

BlackHoles(L24).................................... .......64

QuantumCosmology(E16).............................. ........65

IntroductionToTwistorTheory(E16)................... ............66

Astrophysics 67

AstrophysicalFluidDynamics(M24).................... .............67

StructureandEvolutionofStars(M24).................. .............68

AccretionDiscs(L16)................................ .........68

Galaxies(L24)...................................... .......69

PhysicalCosmology(L24)............................. ..........70

StellarandPlanetaryMagneticFields(L24)............. ................71

I am interested in differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology.

So right now I can't decide what area I want to major in? How do you guys decide what area to specialize?

What subject I should choose so that I can still keep in touch with my favorite topics (differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology) ?

Please help me I am clueless.

I only allowed to take 10 course from the list above and hopefully the course that I choose will be useful in my research for PhD ( still haven't decide what topic).

Thank you for your help. :)

DecisionProblemsinGroupTheory(L24)................. .............5

LieAlgebrasandRepresentationTheory(M24)............ ...............5

ModularRepresentationsofFiniteGroups(L24).......... ................6

Calculusandalgebra(L24)............................ ..........8

Representationsof?nitegroupsofLietype(L24)......... .................8

CommutativeAlgebra(M24)............................ .........9

Non-commutativealgebras(L24)....................... ............9

VonNeumannAlgebras(L24)............................ .........10

Analysis 12

TopologicalGroups(L24)............................. ..........12

TopicsinIn?niteGroups(M16)......................... ...........12

AnalysisontheDiscreteHypercube(L24)— Non–Examinable .................13

IntroductiontoFunctionalAnalysis(M24).............. ................14

ComplexDi?erentialEquations(L24)................... .............15

Ellipticpartialdi?erentialequations(M24)........... ..................15

Combinatorics 17

Combinatorics(M16)................................. .........17

CombinatorialProbability(L16)...................... .............17

HypergraphGames(E8)— Non–Examinable ..........................18

ArithmeticCombinatorics(M16)....................... ............18

GeometryandTopology 19

TheX-raytransformingeometryanddynamics(L24)........ ...............19

AlgebraicTopology(M24)............................. ..........20

Di?erentialGeometry(M24)........................... ..........20

SpectralGeometry(L24).............................. .........21

AlgebraicGeometry(M24)............................. .........22

ComplexManifolds(L24).............................. .........22

AlgebraicGroups(M24)............................... .........24

FibreBundles(L16).................................. ........24

AlgebraicCycles(L24)............................... ..........25

Logic 26

CategoryTheory(M24)................................ ........26

SetTheoryandLogic(L24)............................. .........27

NumberTheory 29

EllipticCurves(L24)................................ ..........29

LocalFields(M16)................................... ........29

ErgodicTheory(L24)................................. ........30

TheIwasawatheoryofellipticcurveswithcomplexmultiplication(L24).............31

AlgebraicNumberTheory(M16)......................... ..........31

ModularFormsandAutomorphicForms(L24)............... ............32

Non-abelianLubin-Tatetheory(M24)— Non–Examinable ...................32

Probability 3

AdvancedProbability(M24)........................... ..........3

StochasticNetworks(L24)............................ ...........3

StochasticLoewnerEvolutions(L16)................... ..............3

StochasticCalculusandApplications(L24)............. ................3

ParticlePhysics,QuantumFieldsandStrings 46

QuantumFieldTheory(M24)............................ .........46

SymmetryandParticlePhysics(M24).................... ............47

StatisticalFieldTheoryandApplications(M24)......... .................48

AdvancedQuantumFieldTheory(L24).................... ...........49

StringTheory(L24).................................. ........49

SupersymmetryandExtraDimensions(L24)............... .............50

StandardModel(L24)................................. ........51

SolitonsandInstantons(E16)......................... ............52

Supergravity(E16).................................. .........53

3

QuantumInformationandQuantumFoundations 54

IntroductiontoQuantumComputation(M16).............. .............54

QuantumInformation,EntanglementandNonlocality(M16). ..................55

PhilosophyofClassicalandQuantumMechanics(M12,L12).. .................55

MathematicalAspectsofQuantumInformationTheory(L24). ..................56

QuantumControl(L16)................................ ........57

RelativityandGravitation 59

Cosmology(M24)..................................... .......59

GeneralRelativity(M24)............................. ..........61

AdvancedCosmology(L16)............................. .........62

ApplicationsofDi?erentialGeometrytoPhysics(L24).... ...................63

BlackHoles(L24).................................... .......64

QuantumCosmology(E16).............................. ........65

IntroductionToTwistorTheory(E16)................... ............66

Astrophysics 67

AstrophysicalFluidDynamics(M24).................... .............67

StructureandEvolutionofStars(M24).................. .............68

AccretionDiscs(L16)................................ .........68

Galaxies(L24)...................................... .......69

PhysicalCosmology(L24)............................. ..........70

StellarandPlanetaryMagneticFields(L24)............. ................71

I am interested in differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology.

So right now I can't decide what area I want to major in? How do you guys decide what area to specialize?

What subject I should choose so that I can still keep in touch with my favorite topics (differential geometry, group theory, a bit of quantum mechanic, some algebra, complex analysis and topology) ?

Please help me I am clueless.

I only allowed to take 10 course from the list above and hopefully the course that I choose will be useful in my research for PhD ( still haven't decide what topic).

Thank you for your help. :)